Gold Interface Research Articles

Gold-etching redox reactions at the gold interface of an ionic liquid monitored using electrochemical surface plasmon resonance

I2/I− redox reaction on the gold interface of an ionic liquid, 1-octyl-3-methylimidazolium bis(nonafluorobutanesulfonyl)amide, has been studied using electrochemical surface plasmon resonance (SPR) to investigate how SPR can sense the dissolution/deposition of gold film accompanied with the two-step processes of the I2/I− redox reaction. The SPR response measured simultaneously with cyclic voltammetry (CV) has clearly shown that SPR can sense the change in the gold film thickness due to the gold dissolution/deposition. The classical least squares method has successfully separated the two contributions to the SPR response: one from the gold thickness and the other from the surface concentration of dissolved redox species. Model simulations for CV and light reflectivity have reproduced the two SPR contributions well. Furthermore, a systematic deviation of the experimental data from the simulation results observed at positive potentials has suggested that the gold dissolution/deposition processes induce the surface roughness change of the gold film on the Angstrom level.

Graphene-Based Opto-Electronic Platform for Ultra-Sensitive Biomarker Detection at Zeptomolar Concentrations.

A ground-breaking graphene-based biosensor designed for label-free detection of immunoglobulin M (IgM) achieving a remarkable concentration of 100 zeptomolar (10-19 m), is reported. The sensor is a two-terminal device and incorporates a millimeter-wide gold interface, bio-functionalized with ≈1012 anti-IgM antibodies and capacitively coupled to a bare graphene electrode through a water-soaked paper strip. In this configuration, few affinity binding events trigger a collective electrostatic reorganization of the protein layer, leading to an extended surface potential (SP) shift of the biofunctionalized Au surface. The SP shift, mediated by electrolyte capacitive coupling, induces a corresponding shift in the Fermi level of graphene. This shifts the graphene phonon frequencies, which are measured by Raman spectroscopy. Decoupling the sensing interface from the transducing graphene layer provides flexibility in surface chemistry modifications, while preserving the graphene integrity. A key aspect of this biosensor is its ability to precisely determine the graphene charge neutrality point from the voltage dependence of phonon frequency shifts, enabling detections of biomarker at unprecedented low concentrations. The integration of graphene with optical probing demonstrates a proof-of-concept and establishes a ground-breaking approach to in situ biomarker detection, setting the stage for a future generation of portable opto-electronic high-performance diagnostic tools for single-marker detection.

Detection of the SARS-CoV-2 nucleoprotein by electrochemical biosensor based on molecularly imprinted polypyrrole formed on self-assembled monolayer.

Herein, we report the development and characterisation of an electrochemical biosensor with a polypyrrole (Ppy)-based molecularly imprinted polymer (MIP) for the serological detection of the recombinant nucleocapsid protein of SARS-CoV-2 (rN). The electrochemical biosensor utilises a Ppy-based MIP formed on a self-assembled monolayer (SAM) at the gold interface to enhance Ppy layer stability on the screen-printed electrode (SPE). Electrochemical impedance spectroscopy (EIS) and square wave voltammetry (SWV) were employed for the electrochemical characterisation of screen-printed gold electrodes (SPGEs) modified with MIP or non-imprinted polymer (NIP) layers. Removing the rN protein template from the MIP layer increased electron transfer and decreased impedance, indicating the specificity of molecular imprinting. The electrochemical biosensor with a Ppy-based MIP exhibited higher sensitivity than the NIP counterpart, demonstrating its potential for selective rN protein detection. The limit of detection 0.4nM and 0.2nM and the limit of quantification 1.3nM and 0.66nM values obtained through SWV and EIS, respectively, highlight the biosensor's ability to detect low target protein concentrations. The specificity test confirmed minimal nonspecific binding, reinforcing the reliability of the novel electrochemical sensor with a Ppy-based MIP.

Achieving nearly 70 cm2/V·s field-effect mobility in single amorphous Ga-In-ZnO thin-film transistors deposited by sputtering process via intermediate patterned metal layer insertion

In this study, we introduce a novel method for enhancing the mobility of amorphous Ga-In-Zn-O (a-GIZO) thin-film transistors (TFTs) by incorporating a patterned metal layer within the a-GIZO single channel. The patterned metal layer comprises either a single layer of aluminum or a combination of aluminum and gold as the bottom and top layers, respectively. TFTs with a single aluminum layer achieved a field-effect mobility of 40.15 cm2/V∙s, significantly higher than the 16.22 cm2/V∙s of standard a-GIZO TFTs. This enhancement is attributed to aluminum’s low Gibbs free energy, which increases oxygen vacancies in the a-GIZO layer and thus improves carrier mobility. Furthermore, when a patterned dual-metal layer consisting of aluminum as the bottom layer and gold as the top layer is used, a field-effect mobility of 69.46 cm2/V∙s is achieved. This improvement is attributed to the low electrical resistivity of gold, which prevents oxidation between the upper gold layer and the a-GIZO layer deposited by sputtering process. Furthermore, this mechanism facilitates the enhancement of the reaction with a lower a-GIZO layer. The unique characteristics of gold prevent oxidation between the a-GIZO and gold interface, thereby promoting favorable interactions between Al and the underlying a-GIZO layer. Our findings demonstrate that strategically inserted patterned metal layers can significantly boost mobility of a single a-GIZO TFT while maintaining device stability, offering a promising approach for advanced display technologies.

Properties of Sn-3.0Ag-0.5Cu solder joints under various soldering conditions: Reflow vs. Laser vs. Intense Pulsed Light soldering

In this study, the properties of solder joints were compared after bonding process using different energy sources. Various soldering methods were employed, including reflow, laser, and Intense Pulsed Light (IPL) soldering. When reflow soldering was performed for a relatively long time, coarse solder microstructures and interfacial intermetallic compound (IMC) grains were formed. Laser and IPL soldering, which have rapid heating/cooling times, formed fine solder microstructure and thin interfacial IMCs. Then, it was confirmed that Cu6Sn5 and Cu3Sn IMCs were formed at the SAC305/OSP (organic solderability preservative) interface and (Cu,Ni)6Sn5, Ni–Sn–P, and Ni3P were formed at the SAC305/ENEPIG (electroless nickel electroless palladium immersion gold) interface. An observation of the IMC grain morphology under various soldering conditions revealed that (Cu,Ni)6Sn5 was formed on the ENEPIG substrate, which was polygonal and smaller than on the OSP substrate. The shear strength of the joint increased in the order of reflow, laser, and IPL soldering. Additionally, ductile fractures occurred under all conditions. The IPL soldering joint had a thinner IMC compared to reflow soldering, and moderate interface roughness and bonding area compared to laser soldering. Based on the obtained results, a next-generation IPL soldering method is proposed to improve the properties of Sn-3.0Ag-0.5Cu solder joints.

Chiroptical Activity Amplification of Chiral Metal Nanoclusters via Surface/Interface Solidification.

It remains a grand challenge to amplify the chiroptical activity of chiral metal nanoclusters (NCs) although it is desirable for fundamental research and practical application. Herein, we report a strategy of surface/interface solidification (SIS) for enhancing the chiroptical activity of gold NCs. Structural analysis of [Au19(2R,4R/2S,4S-BDPP)6Cl2]3+ (BDPP is 2,4-bis(diphenylphosphino)pentane) clusters reveals that one of the interfacial gold atoms is flexible between two sites and large space is present on the surface, thus hampering chirality transfer from surface chiral ligands to metal core and leading to low chiroptical activity. Following SIS by filling the flexible sites and replacing chlorides with thiolate ligands affords another pair of [Au20(2R,4R/2S,4S-BDPP)6(4-F-C6H4S)2]4+, which shows a more compact and organized structure and thus an almost 40-fold enhancement of chiroptical activity. This work not only provides an efficient approach for amplifying the chiroptical activity of metal nanoclusters but also highlights the significance of achiral components in shaping chiral nanostructures.

Theoretical and experimental investigations of enhanced carbon nanotube-gold interface conductivity through nitrogen doping.

It is necessary to establish high-quality contact between carbon nanotubes and metals in carbon-based devices. However, how to control and reduce contact resistance still remains unsolved. In this study, the effect of N doping in single-walled carbon nanotubes on the contact resistance with gold was studied by combining theoretical calculation with experimental methods. The theoretical results indicate that nitrogen doping in carbon nanotubes can control the bottom of the carbon nanotube conduction band downward, the Fermi level enters the conduction band, the height of the Schottky barrier between the bottom of the carbon nanotube conduction band and the gold Fermi level decreases, and the increase in doping concentration leads to the decrease of Schottky barrier width. As a result, the conductivity between the gold and carbon nanotube interface is enhanced. During experiments, the carrier density and the current of the gold and carbon nanotube device increase gradually with the increase in N doping concentration and a good electron transport channel is established between the gold and carbon nanotubes. The high-quality contact is crucial to reducing the size, improving the performance, and reducing the power consumption of carbon-based devices.

TiO2 nanorod/nanotube interface reconstruction and synergistic role of oxygen vacancies and gold in H–Au–TiO2 NR/NT for photoelectrochemical bacterial inactivation and water splitting

Photoelectrochemical (PEC) water splitting by semiconductor photoanodes is limited by sluggish water oxidation kinetics coupled with serious charge recombinations. In this paper, an effective strategy of TiO2 nanorod/nanotube nanostructured interface reconstruction, oxygen vacancies and surface modification were employed for stability and efficient charge transport in the photoanodes. Successive anodization and hydrothermal routes were adopted for the TiO2 NR/NT photoanodes interface reconstruction, followed by Au nanoparticles/clusters (Au NP) loading and hydrogen treatment. This resulted in H–Au–TiO2 NR/NT photoanodes. A three-dimensional structure of TiO2 NR on TiO2 NT/Ti foil nanotubes achieved the highest photocurrent density (1.42 mA cm−2 at 0.3 V vs. Ag/AgCl). The optimal oxygen vacancies and Au NP loading on TiO2 NR/NT exhibited 1.62 mA cm−2 photocurrent density at 0.3 V vs. Ag/AgCl in H–Au–TiO2 NR/NT photoelectrode, which is eight times higher than the TiO2 NT/Ti foil. TRPL analyses confirm the hydrogen treatments to TiO2 exhibited the emission lifetime (46 ns) in the H–Au–TiO2 NR/NT photoanodes due to newly formed lower Ti3+-related trapped electron states and Au NP. The optimum H–Au (4)–TiO2 NR/NT photoanodes achieved 95% photoelectrochemical (PEC) bacterial inactivation and effective PEC water splitting with (278 and 135.4) μmol of hydrogen and oxygen generation, respectively. In this study, oxygen vacancies combined with gold particles and interface reconstruction provide an innovative way to design effective photoelectrodes.

Tuneable interphase transitions in ionic liquid/carrier systems via voltage control

The structure and interaction of ionic liquids (ILs) influence their interfacial composition, and their arrangement (i.e., electric double-layer (EDL) structure), can be controlled by an electric field. Here, we employed a quartz crystal microbalance (QCM) to study the electrical response of two non-halogenated phosphonium orthoborate ILs, dissolved in a polar solvent at the interface. The response is influenced by the applied voltage, the structure of the ions, and the solvent polarizability. One IL showed anomalous electro-responsivity, suggesting a self-assembly bilayer structure of the IL cation at the gold interface, which transitions to a typical EDL structure at higher positive potential. Neutron reflectivity (NR) confirmed this interfacial structuring and compositional changes at the electrified gold surface. A cation-dominated self-assembly structure is observed for negative and neutral voltages, which abruptly transitions to an anion-rich interfacial layer at positive voltages. An interphase transition explains the electro-responsive behaviour of self-assembling IL/carrier systems, pertinent for ILs in advanced tribological and electrochemical contexts.

Investigation of Hexylamine Adsorption on Gold in Perchloric Acid

The adsorption of hexylamine at the solution–gold interface in 1 M HClO4 in the presence of 0.1 M Fe2+ and 0.1 Fe3+ was studied by potentiodynamic, chronoamperometric and EIS methods. The main kinetic characteristics of the oxidation-reduction reaction iron ions (exchange current density, transfer coefficient, diffusion coefficients of iron ions) were determined. It was shown that the physical adsorption of hexylamine on gold can be described by the Dhar–Flory–Huggins isotherm. The values of the adsorption constant and the Gibbs free adsorption energy were obtained. A comparison of the free adsorption energy at these interfaces with the interaction energies of hexylamine and water molecules, and hexylamine molecules with each other was carried out. It was shown that hexylamine adsorption at all of these interfaces is due mainly to the hydrophobic effect of the interaction of hexylamine and water molecules.

Multimode hybrid gold-silicon nanoantennas for tailored nanoscale optical confinement.

High-index dielectric nanoantennas, which provide an interplay between electric and magnetic modes, have been widely used as building blocks for a variety of devices and metasurfaces, both in linear and nonlinear regimes. Here, we investigate hybrid metal-semiconductor nanoantennas, consisting of a multimode silicon nanopillar core coated with a gold layer, that offer an enhanced degree of control over the mode selection and confinement, and emission of light on the nanoscale exploiting high-order electric and magnetic resonances. Cathodoluminescence spectra revealed a multitude of resonant modes supported by the nanoantennas due to hybridization of the Mie resonances of the core and the plasmonic resonances of the shell. Eigenmode analysis revealed the modes that exhibit enhanced field localization at the gold interface, together with high confinement within the nanopillar volume. Consequently, this architecture provides a flexible means of engineering nanoscale components with tailored optical modes and field confinement for a plethora of applications, including sensing, hot-electron photodetection and nanophotonics with cylindrical vector beams.

Temperature-Dependent Coalescence of Individual Nonpolar Gold Nanoparticles in Liquid

Self-assembled nanoparticles (NPs) in superlattices are in close contact. Their dense packing and the proximity of aligned facets can facilitate coalescence and enable crystal lattices to fuse at temperatures below the bulk melting point. This phenomenon could be applied in nanodevice manufacture. We study NP fusion in superlattices in liquid and dry environments at controlled temperatures using electron microscopy at minimized electron doses. We found that coalescence of self-assembled gold NPs (AuNPs, diameter 8.1 ± 0.4 nm) depended on their arrangement. A double layer of AuNPs in a hexagonally close packed superlattice started to coalesce within 2 min at a temperature of 70 °C in cyclohexane but remained stable for 30 min at 98 °C when it was dry. AuNPs assembled in hexagonal monolayers coalesced after 5 min at 75 °C in cyclohexane. The mobility of the ligand shells and the interfacial gold atoms and the sparse ligand coverage on (111) facets likely facilitated this AuNP coalescence at low temperatures.

A cold-responsive liquid crystal elastomer provides visual signals for monitoring a critical temperature decrease.

Critical temperature indicators have been extensively utilized in various fields, ranging from healthcare to food safety. However, the majority of the temperature indicators are designed for upper critical temperature monitoring, indicating when the temperature rises and exceeds a predefined limit, whereas stringently demanded low critical temperature indicators are scarcely developed. Herein, we develop a new material and system that monitor temperature decrease, e.g., from ambient temperature to the freezing point, or even to an ultra-low temperature of -20 °C. For this purpose, we create a dynamic membrane which can open and close during temperature cycles from high temperature to low temperature. This membrane consists of a gold-liquid crystal elastomer (Au-LCE) bilayer structure. Unlike the commonly used thermo-responsive LCEs which actuate upon temperature rise, our LCE is cold-responsive. This means that geometric deformations occur when the environmental temperature decreases. Specifically, upon temperature decrease the LCE creates stresses at the gold interface by uniaxial deformation due to expansion along the molecular director and shrinkage perpendicular to it. At a critical stress, optimized to occur at the desired temperature, the brittle Au top layer fractures, which allows contact between the LCE and material on top of the gold layer. Material transport via cracks enables the onset of the visible signal for instance caused by a pH indicator substance. We apply the dynamic Au-LCE membrane for cold-chain applications, indicating the loss of the effectiveness of perishable goods. We anticipate that our newly developed low critical temperature/time indicator will be shortly implemented in supply chains to minimize food and medical product waste.

Gold Atomic Layers and Isolated Atoms on MoC for the Low-Temperature Water Gas Shift Reaction

Au 2–4 atomic layers, monolayers, and isolated atoms were generated by redispersing a Au particle (8 nm) during MoO3 carburization to α-MoC with a CH4/H2 mixture at 600–750 °C. The spherical Au particle initially wetted on the developing molybdenum carbides, reshaped into large thin films, then decomposed to smaller islands, and finally cracked into 2–4 atomic layers at 600 °C. These layered Au species further split into isolated atoms when carburized at 750 °C, which could be reversed into monolayers and 1–2 atomic layers by H2-treatment at 630–650 °C, followed by activation with a CH4/H2 mixture at 590 °C. When tested for the low-temperature water gas shift reaction, the 2–4 atomic layers possessed a much higher activity than the monolayers and isolated atoms. Interestingly, the specific reaction rate showed a volcano-type pattern with respect to the coordination number of Au–Au in the size-specified gold species, where the Au 2–4 atomic layers having a Au–Au coordination number of 7.7 were intrinsically more active. Detailed structural analysis, by STEM and EXAFS, identified that the interfacial gold atom coordinated simultaneously with the Mo atom in MoC and Au atoms in the layers.

Electrosynthesis of poly(2,5-dimercapto-1,3,4-thiadiazole) films and their composites with gold nanoparticles at a polarised liquid|liquid interface

The organosulfur compound 2,5-dimercapto-1,3,4-thiadiazole (DMcT) finds widespread applications in batteries, lubricant fluids, heavy metal ion sensors, waste-water purification and as a biocide. In this article, we demonstrate the untapped versatility inherent to using biphasic systems for electrosynthesis by showcasing several successful approaches to the electrosynthesis of poly(DMcT) films at a polarised interface between two immiscible electrolyte solutions (ITIES) by cyclic voltammetry (CV) cycling using either I 2 , Hg 2+ or O 2 as the oxidising agents. AC voltammetry is demonstrated as an effective in situ method to monitor poly(DMcT) film formation by I 2 or Hg 2+ as a function of the aqueous electrolyte anion and pH. DMcT is further shown to act as a binder molecule to promote interfacial gold nanoparticle (AuNP) assembly into floating films at an immiscible liquid|liquid (L|L) interface. Exploiting the electrocatalysis of DMcT oxidation by O 2 in the presence of adsorbed interfacial AuNPs yields AuNP/poly(DMcT) composite films. Raman spectroscopy suggests the latter were a coordination polymer of poly(DMcT) with AuNPs and surface enhanced Raman spectroscopy (SERS) active. The dielectric nature of the poly(DMcT) films suppresses the capacitance at the ITIES, yet the AuNP/poly(DMcT) films show a very high interfacial capacitance, with an ability to efficiently adsorb cations. Thus, these films open opportunities to selectively modulate the interfacial capacitance, potentially forming the basis of novel “soft” capacitors at a polarised L|L interface.

Amorphous Copper‐modified Gold Interface Promotes Selective CO2 Electroreduction to CO

AbstractElectroreduction of CO2 into valuable chemicals exhibits promising application potentials. Herein, a kind of nano‐porous AuCu foam which possesses amorphous copper (Cu)‐modified gold (Au) interface was designed for highly selective electroreduction CO2 into CO. As‐obtained Au0.95Cu0.05 foam exhibits a Faradaic efficiency (FE) of 99.5 % for CO with a current density of 31.3 mA cm−2. Compared with other Au‐based electrocatalysts, Au0.95Cu0.05 foam shows a lower overpotential of 240 mV. The improvements in activity and selectivity of the AuCu foam might be attributed to the synergistic effect between the highly dispersed amorphous Cu and the matrix of Au. Detailed characterization indicates that the twisty nanowire morphology imparts multiple reactive sites on the electrode surface. The study demonstrates that amorphous Cu on the AuCu foam surface can boost CO2 activation by modifying the surface geometry and electronic structure. This finding provides a new strategy of modifying the metal interface to construct electrocatalyst.

Interfacial Selective Study on the Gelation Behavior of Aqueous Methylcellulose Solution via a Quartz Crystal Microbalance.

It is important to understand the interfacial structure and physical properties of a polymer material to improve its function. In this study, we used a quartz crystal microbalance (QCM) and neutron reflectivity (NR) measurements to evaluate the viscoelasticity and structure of an aqueous methylcellulose solution near the gold interface. The apparent shear modulus, which was calculated from the complex frequency, was used to assess gelation behavior. The apparent shear modulus determined via the QCM suggested high-frequency rheological properties that reflected the relaxation of skeletal stretching and rotational motion of polymer segments, as well as cooperative motion of the various functional groups. The gelation temperature was found to be lowered at the interface in comparison with that of the bulk. It is suggested that the QCM can evaluate the shear modulus accompanying the gelation near the interface. The interfacial segregation on the gold substrate caused by the surface free energy and long-range van der Waals interaction was observed from NR measurements.

Numerical study of the effects of Brownian motion and interfacial layer on the viscosity of nanofluid (Au-H2O)

Untilnow, the contribution of nanoscale mechanisms to shear viscosity enhancement of nanofluid have only been postulated in experiments. This paper presents the study of equilibrium molecular dynamics simulation to explore the nanoscale mechanisms such as Brownian motion of gold nanoparticles and interfacial layer at water – gold interface, and to investigate their effects on the shear viscosity enhancement in nanofluid (Au-H2O). Moreover, the computationally efficient model of TIP4P/2005 model was used to model the water, and the shear viscosity has been calculated through the molecular dynamics coupled with Green-Kubo formula. In addition, this numerical study was performed in the temperature range of 288 K to 338 K and at different gold volume fractions of 2.6%, 3.2%, 4.0% and 5.2%. The results have revealed that the decreasing shear viscosity of nanofluid (Au-H2O) with increasing the temperature is due to an increase in the Brownian motion, and that the interfacial layer at water – gold interface contributes to shear viscosity enhancement of aqueous nanofluid containing the gold nanoparticles. Furthermore, the results have shown that the formation of a liquid layer at the pure water-gold interface is not affected by that the Brownian motion of gold nanoparticles in pure water.

Effects of anions and alkyl chain length of imidazolium-based ionic liquids at the Au (111) surface on interfacial structure: a first-principles study

The interfacial structure and adsorption mechanism of imidazolium-based ionic liquids (ILs) on Au (111) surface were investigated via first-principles calculation. Electron density analysis and Bader charge analysis were used to explore the electronic structure of Au (111)-ILs interface. Computations show that the alkyl chain length and anions play a significant role in designing Au (111)-ILs interfacial structure. On the one hand, the stability of interface and adsorption energy tend to be enhanced as the alkyl chain length increases. It attributes to the methylene group of alkyl chain which could easily anchor on the gold interface. On the other hand, the difference in anions makes the adsorption behavior quite different. The adsorption energy follows the order: [Cnmim][Br] > [Cnmim][Cl] > [Cnmim][TFSA] > [Cnmim][OAc] > [Cnmim][PF6] > [Cnmim][BF4]. The nonfluorinated ILs (containing Br, Cl, and O atoms of anions) always have a drastic charge transfer among gold-ILs interface. However, the larger van der Waals (vdWs) volumes of the fluorinated anions have a more diffused electron density which lead to the relatively weak interaction. To sum up, a detailed and systematic investigation of the variation of anions and alkyl chain length of ILs which will affect the interfacial structure is fully studied. The above study could be helpful to understand electrode-electrolyte microscopic interface and design of functional materials for energy storage.

Large-Area, Two-Dimensional MoS2 Exfoliated on Gold: Direct Experimental Access to the Metal-Semiconductor Interface.

Two-dimensional semiconductors such as MoS2 are promising for future electrical devices. The interface to metals is a crucial and critical aspect for these devices because undesirably high resistances due to Fermi level pinning are present, resulting in unwanted energy losses. To date, experimental information on such junctions has been obtained mainly indirectly by evaluating transistor characteristics. The fact that the metal–semiconductor interface is typically embedded, further complicates the investigation of the underlying physical mechanisms at the interface. Here, we present a method to provide access to a realistic metal–semiconductor interface by large-area exfoliation of single-layer MoS2 on clean polycrystalline gold surfaces. This approach allows us to measure the relative charge neutrality level at the MoS2–gold interface and its spatial variation almost directly using Kelvin probe force microscopy even under ambient conditions. By bringing together hitherto unconnected findings about the MoS2–gold interface, we can explain the anomalous Raman signature of MoS2 in contact to metals [ACS Nano. 7, 2013, 11350] which has been the subject of intense recent discussions. In detail, we identify the unusual Raman mode as the A1g mode with a reduced Raman shift (397 cm–1) due to the weakening of the Mo–S bond. Combined with our X-ray photoelectron spectroscopy data and the measured charge neutrality level, this is in good agreement with a previously predicted mechanism for Fermi level pinning at the MoS2–gold interface [Nano Lett.14, 2014, 1714]. As a consequence, the strength of the MoS2–gold contact can be determined from the intensity ratio between the reduced A1greduced mode and the unperturbed A1g mode.